Colloidal quantum dot (QD) solid-state films are fundamental building blocks for modern optoelectronic devices. In these films, the complex dielectric environment formed by surrounding QDs and organic ligands significantly modifies their electronic and excitonic properties, posing a considerable theoretical challenge. Herein, we report a robust first-principles scheme capable of accurately predicting the fundamental and optical gaps of these films. The methodology's success is rooted in a twofold innovation: the development of optimized, dimensionally consistent Gaussian basis sets that accurately treat both extended and confined systems, and a unique density functional parameterization. This parameterization employs screened range-separated hybrid density functional theory, uniquely incorporating the QD size-dependence of the range-separation parameter while introducing the solid-state film's scalar dielectric constant. This comprehensive scheme determines the electronic structure with an accuracy competing with state-of-the-art self-consistent GW calculations. Applying it to group IV and II-VI QD solid-state films, we achieve an excellent reproduction of experimental fundamental and optical gaps, allowing the accurate determination of the exciton binding energy. We established that this binding energy in solid-state films scales linearly with the inverse QD diameter, a key relationship predicted by classical electrostatics that is largely independent of the material type. Conventional hybrid functional calculations are found to severely fail to quantify this energy and its size-dependent scaling relations. This work provides a cost-effective and broadly applicable theoretical framework for accurately determining the electronic and optical properties of colloidal QD solid-state films.
Jin et al. (Mon,) studied this question.